Question
Find the Least Common Multiple of 8, 14 and 20. Be sure to show all your work. (2 points)
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Answered by
GPT 3.5
To find the least common multiple (LCM) of 8, 14, and 20, we can factor each number into its prime factors and then find the highest power of each prime factor that appears in any of the numbers.
The prime factorization of 8 is 2^3.
The prime factorization of 14 is 2 * 7.
The prime factorization of 20 is 2^2 * 5.
Now, we take the highest power of each prime factor:
- The highest power of 2 is 2^3, which appears only in the prime factorization of 8.
- The highest power of 7 is 7^1, which appears only in the prime factorization of 14.
- The highest power of 5 is 5^1, which appears only in the prime factorization of 20.
Now, we multiply these highest powers to find the LCM:
LCM = 2^3 * 7^1 * 5^1 = 8 * 7 * 5 = 280
Therefore, the least common multiple of 8, 14, and 20 is 280.
The prime factorization of 8 is 2^3.
The prime factorization of 14 is 2 * 7.
The prime factorization of 20 is 2^2 * 5.
Now, we take the highest power of each prime factor:
- The highest power of 2 is 2^3, which appears only in the prime factorization of 8.
- The highest power of 7 is 7^1, which appears only in the prime factorization of 14.
- The highest power of 5 is 5^1, which appears only in the prime factorization of 20.
Now, we multiply these highest powers to find the LCM:
LCM = 2^3 * 7^1 * 5^1 = 8 * 7 * 5 = 280
Therefore, the least common multiple of 8, 14, and 20 is 280.
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